Construction of microscopic boson states and their relevance for IBM-2

Abstract

Abstract We investigate four methods for the construction of collective shell model states which may be mapped onto boson states of the IBM-2. These methods use, as building blocks for the wave functions, particle-particle pair operators, particle-hole operators, pair operators with seniority projection and energy-weighted quadrupole operators. It is demonstrated that one obtains stronger collectivity with the energy-weighted quadrupole operator than with the other methods. On the basis of a comparison of calculated and empirical IBM-2 interaction parameters we can rule out the seniority projection method. This implies that particle-particle and particle-hole approaches difler. The ratios between quadrupole matrix elements of the microscopic boson states appear to be similar to the IBM predictions. For states corresponding to those with two d-bosons coupled to J = 0 there is a smaller quadrupole matrix element when subshells with small angular momenta dominate near the Fermi level. Especially for this type of states the collective quadrupole space will be larger than represented in the IBM, however, which may compensate the smaller proton-neutron quadrupole coupling. The calculated bare quadrupole interaction between like bosons is found to be weak.

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